LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION - STATISTICS
FIRST SEMESTER – November 2008
BA 23
ST 1812 - STATISTICAL COMPUTING - I
Date : 13-11-08
Time : 1:00 - 4:00
Dept. No.
Max. : 100 Marks
Answer any THREE questions. Each carries THIRTY FOUR marks.
1. (a). Fit a distribution of the type
P(x) = (1/2) [P1(x) + P2(x)]
where P1(x) = (e –μ μ x ) / x! ; x = 0,1,2, …, μ >0
and P2(x) = (e –λ λ x ) / x! ; x = 0,1,2, …, λ >0
for the following data on the frequency of accidents during 106 weeks in
Chennai:
No. of accidents : 0
1
2
3
4
5
No. of weeks
: 26
46
20
6
5
3.
Also test the goodness of fit at 5% level of significance.
(18)
(b) In a population containing 539 live birds of same weight and age , the birds
were divided into 77 equal groups. They were then given a stimulus to increase
the growth rate . The following data gives the frequency distribution of those
with significant weight at the end or 6 weeks. Fit a truncated binomial
distribution and test the goodness of fit at 5% of level of significance.
No. of birds : 1
Frequency : 7
2
16
3
22
4
18
5
9
6
3
7
2
(16)
2. (a). Find a g-inverse of the following matrix.
2
2
5
3
2
3
3
2
3
3
7
4
3
2
9
7
1
7
2
3
(17)
(b) Find the characteristic roots and vectors of the following matrix:
1
1
0
1
-1
1
1
2
1
( 17)
3. (a) Generate a random sample of size 15 from Cauchy distribution with p.d.f.
f(w) = (1/π) [ λ / { λ 2 + (w – θ) 2 } ] , taking θ = 50 and λ =5. 14)
1
(b) Verify whether or not the following matrix is positive definite:
12
4
-4
4
12
4
-4
4
20
(10)
(c) Find the rank of the given matrix A by performing row operations:
3
4
2
2
3
1
3
5
1
1
2
0
(10)
4. Consider the following data for a dependent variable representing repair time in hours and two
independent variables representing months since last service and type of repair.
Customer
Months since
Type of Repair
Repair time
last service
in hours
1
2
1
2.9
2
6
0
3.0
3
8
1
4.8
4
3
0
1.8
5
2
1
2.9
6
7
1
4.9
7
9
0
4.2
8
8
0
4.8
9
4
1
4.4
10
6
1
4.5
Using these data, develop an estimated regression equation relating repair time in hours to months
since last service and type of repair. Estimate the repair time if months since last service = 12 and
type of repair = 1.
5. The following table gives the annual return, the safety rating (0=riskiest, 10 = safest) and the annual
expense ratio for 10 foreign funds (Mutual funds, March 2006).
Foreign Funds
Safety Rating
Annual Expense
Annual
Ratio (%)
Return (%)
1
7.1
1.5
49
2
7.2
1.3
52
3
6.8
1.6
89
4
7.1
1.5
58
5
6.2
2.1
131
6
7.4
1.8
59
7
6.5
1.8
99
8
7.0
0.9
53
9
6.9
1.7
77
10
7.7
1.2
61
a) Use F-test to determine the overall significance of the relationship at 0.05 level of significance.
b) Use t-test to determine the significance of each independent variable at 5 % level of significance.
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